Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11 ft.
h
Which equation gives the volume of the sphere?

Answer 1

Answer:

$V_{sphere}=\frac{2V_{cylinder}}{3}$

$V_{sphere}=7.33$

Step-by-step explanation:  

Information we have:

Volume of the cylinder: $11ft$

The formula for volume of a cylinder is:

$V_{cylinder}=\pi r^2h$

where $r$ is the radius and and h is the height

and the formula for the volume of a sphere is:

$V_{sphere}=\frac{4\pi r^3}{3}$

we dont have the height of the sphere in the formula but the height is double the radius:

$h=2r$

thus we manipulate the formula for the volume to get a 2r and the substitute with h:

$V_{sphere}=\frac{2*2\pi r^2*r}{3} \\V_{sphere}=\frac{2\pi r^2(2r)}{3}$

and we substitute that $h=2r$

$V_{sphere}=\frac{2\pi r^2h}{3}$

the value $r^2h$ must be equal for the sphere and for the cylinder.

We clear $r^2h$ from the volume of the cylinder

$V_{cylinder}=\pi r^2h$

• $r^2h=\frac{V_{cylinder}}{\pi}$

and we do the same for the volume of the sphere:

$V_{sphere}=\frac{2\pi r^2h}{3}$

• $r^2h=\frac{3V_{sphere}}{2\pi}$

and we equal these two values for $r^2h$  since we are told the radius and the height are the same:

$\frac{V_{cylinder}}{\pi}=\frac{3V_{sphere}}{2\pi}$

and finally, we clear for the volume of the sphere:

$V_{sphere}=\frac{V_{cylinder}*2\pi}{3\pi} \\V_{sphere}=\frac{2V_{cylinder}}{3}$this is the general expression.

and considering the volume of the cylinder is 11ft:

$V_{sphere}=\frac{2*11}{3}\\ V_{sphere}=7.33$

Answer 2

Answer:

C

Step-by-step explanation: